Can anyone explain the order of these signs please?

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SUMMARY

The discussion centers on understanding the order of signs in loop equations related to Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). The participant expresses confusion regarding the initial sign arrangement in the equations I3=I1+I2, despite grasping the fundamental principles of KCL and KVL. They reference a specific resource from the University of Arkansas at Little Rock that clarifies these concepts. The participant seeks clarification on the sign order, indicating that existing textbooks and online examples do not align with their understanding.

PREREQUISITES
  • Understanding of Kirchhoff's Current Law (KCL)
  • Understanding of Kirchhoff's Voltage Law (KVL)
  • Basic knowledge of simultaneous equations
  • Familiarity with electrical circuit analysis
NEXT STEPS
  • Review the resource provided at the University of Arkansas at Little Rock for detailed explanations on sign conventions.
  • Study examples of loop equations in electrical circuits to see varied approaches to sign ordering.
  • Practice solving simultaneous equations in the context of circuit analysis.
  • Explore additional textbooks or online courses focused on advanced circuit analysis techniques.
USEFUL FOR

Students studying electrical engineering, educators teaching circuit analysis, and anyone seeking to deepen their understanding of KCL and KVL in practical applications.

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KCL DIAGRAM.JPG

KCL.JPG


Homework Statement


Create two loop equations.

Homework Equations


I3=I1+I2

The Attempt at a Solution


The solution is given but I do not understand why the signs are ordered as they are.

I understand that in KCL the sum of the currents flowing towards the junction are equal to the sum of the currents moving away.

I also understand that in KVL the sum of the voltage drops is equal to zero.

The example combines these two methods and then goes on to solve by simultaneous equations which I can follow ok.

My problem is with the initial order of the signs (highlighted in yellow). Can anyone explain these please?
My textbooks and examples online seem to approach it slightly differently and I just can't figure it out.
I'm going round and round with it, getting nowhere.
I've just added the images to the post as I see they are difficult to deal with the other way.
 
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Thanks so much for that, it's an excellent piece on the subject. Great resource, thanks again!
 

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